Nature Reserve

In a Nature Reserve and Whildlife Park, there are
$N$ environmental
monitoring stations to monitor temperature, atmospheric
pressure, humidity, fire, water quality, etc. Each station,
labeled from $1$ to
$N$, uses solar panels to
self-supply energy for its operations. There is a communication
network consisting of several 2-way communication channels
between pairs of stations. All stations are connected via this
communication network.

To process data at each station, the Nature Reserve and
Wildlife Park needs to install a Smart Data Analysis program
(with the size of $L$
bytes) to all environmental monitoring stations. The program is
initially installed directly to $S$ stations, then broadcasted to and
installed in all other stations via the communication
network.

To save energy, all communication channels are initially in
an idle state and its need to be activated to send information.
It takes ${E}_{ij}$ energy
units to activate the communication channel between station
$i$ and station
$j$. Once a channel is
activated, it takes one energy unit to transmit one byte via
this channel.

Your task is to determine the minimum energy units required
to send the Smart Data Analysis program to all stations from
the initial $S$
station.

Input

The input consists of several datasets. The first line of
the input contains the number of datasets, which is a positive
number and is not greater than $20$. The following lines describe the
datasets.

Each dataset is described by the following lines:

The first line contains four positive integers: the
number of environmental monitoring stations N, the number
of 2-way communication channels $M$, the size of the program
$L$ (in bytes), and
the number of initial stations $S$$(1 \leq S \leq N \leq {10}^{4}, 1 \leq M
\leq {10}^{6}, M \leq \frac{N*(N-1)}{2}, 1 \leq L \leq
{10}^{6})$.

Each of the following $M$ lines contains three positive
integers $i, j$ and
${E}_{ij}$ to denote
that there is a 2-way communicataion channel between
station $i$ and
station $j$, and it
takes ${E}_{ij}$
energy units to activate this channel $({E}_{ij} \leq {10}^{6})$.

Output

For each data set, write in one line the minimum energy
units required to send the Smart Data Analysis program to all
stations from the initial $S$ stations.